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Although some of the linear curve fitting techniques provide improvements over the classical least squares fit algorithm, most of them cannot globally stabilize majority of data sets, and are not robust enough to handle moderate levels of noise or missing data. In this paper, we apply “ridge regression regularization” to strengthen the stability and robustness of a linear fitting method, 3L fitting algorithm, while maintaining its Euclidean invariance.

As ArF process will be substituted for KrF process at below 0.13 um node, it is time to study CD budget of mask error in ArF lithography. The purpose of this study is to investigate printability of ArF mask defects and corresponding effective specification in repeating cell. Mask defects in regularly repeated pattern were classified as point defect, line defect, and are defect, for convenience's sake, according to their sizes and lithographic explanations. Based on such classification, test reticle (ArF attenuated PSM) was manufactured in our captive mask shop. After exposed at a nominal dose and e-beam cured, each defects was inspected to extract effective specification for ArF process. MNPD (maximum non-printable defect) sizes of various duty patterns were manifested in point defect. In line defect and area defect, as the base pattern CD and duty ratio changed, the slope (MEF) of linear fitting was obtained. Maximum CD deviation from mean CD could be calculated from it. Mask CD budget was considered as 50% of total wafer CD error (10% of target) for mask spec generation. Experimental result was compared with DAIM (diffused aerial image model)-based simulation result because experiment had the error that arose from e-beam curing.

A copolymer containing vinylcyclohexane (VCH) and N-vinyl-2-pyrrolidone (VP) at different compositions was synthesized and characterized. The monomer reactivity ratios (MRR) were estimated by using the classical Fineman–Ross and Kelen–Tudos linear fitting methods. These parameters were also estimated using a nonlinear computational fitting procedure, known as reactivity ratios error in variable model (RREVM). In this case, the values of MRR are rVP=2.2 and rVCH=0.0. Composition shifts and MRR values for (vinylcyclohexane-co-N-vinyl-2-pyrrolidone) copolymer (VCH-co-VP) are interpreted in terms of the relative comonomeric structures. A copolymer with zones containing VP blocks with isolated units of VCH between them is obtained. The presence or absence of the resonance stabilization effect is taken into account. The results are compared with those of similar related copolymeric systems.

Purpose: The purpose of this study is to evaluate inter- and intra-fractional dose variations resulting from head position deviations for patients treated with the Extend relocatable frame utilized in multi-fraction Gamma Knife radiosurgery (GKRS). While previous reports characterized the residual setup and intra-fraction uncertainties of the system, the dosimetric consequences have not been investigated. Methods: A digital gauge was used to measure the head position of 16 consecutive Extend patients (62 fractions) at the time of simulation, before each fraction, and immediately following each fraction. Radial inter-fraction (difference between simulation and pre-fraction positions) and intra-fraction (difference between post-fraction and pre-fraction positions) shifts in patient position were calculated. Planned dose distributions were shifted by the offset to determine the time-of- treatment dose. Variations in mean and maximum target and organ at risk (OAR) doses as a function of positional shift were evaluated. Results: The mean radial inter-fraction shift was 0.64 mm (SD: 0.25, maximum: 1.17). The mean intra-fraction shift was 0.39 mm (SD: 0.25, maximum: 1.44). The mean target dose variation was 0.66% (SD: 1.15%, maximum: 5.77) for inter-fraction shifts and 0.26 % (SD: 0.34, maximum: 1.85) for intrafraction shifts. The maximum OAR dose variation: 7.15% (SD: 5.73, maximum: 30.59) for inter-fraction shifts and 4.07% (SD: 4.22, maximum: 17.04) for intra-fraction shifts. Linear fitting of maximum OAR dose variations as a function of position yielded dose deviations of 11.1%/mm for inter-fractional shifts and 9.3 %/mm for intra-fractional shifts. Conclusion: While positional uncertainties when performing multi-fraction Gamma Knife radiosurgery are small (

A highly sensitive fluorescent probe (1) based on styrylcyanine dye for Cu2+ and Pb2+ has been developed. Probe 1 exhibited fluorescent turn-off sensing ability to Cu2+. On the other hand, 1 displayed ratiometric fluorescent response towards Pb2+ with a distinct fluorescent color change from blue to orange. The 1H NMR titrations revealed that the fluorescent response of 1 to Cu2+ and Pb2+ is triggered by the interaction of the pyridine unit and the metal ion. Detection limits of 1 to Cu2+ or Pb2+ were calculated as 1.24 and 3.41 × 10−6 M, respectively, by standard deviation and linear fitting. Furthermore, 1 can also be used as a sensor for detection of Cu2+ and Pb2+ in a test strip.

Dynamic magnetic resonance imaging (MRI) with rapid sequential image acquisition after bolus injection of gadolinium-diethylene triaminepentaacetic acid (Gd-DTPA) can be used to differentiate benign from malignant lesions. Approximately 84% of malignant tumors exhibited slope values (the slope of the contrastenhancement-over-time curve) higher than 30% per minute; 72% of benign tumors showed slopes lower than 30% per minute [1]. Both benign and malignant tumors showed some overlap resulting in an accuracy of approximately 80 %. The slope values of the time intensity curve of postcontrast dynamic sequences and peak enhancement rates were calculated during the first minute after contrast administration on a pixel-by-pixel basis using a linear fitting algorithm.

Trends in Italian total cloud amount are analysed for the period 1951-1996. The data are a set of 35 station records that were extracted from the 3-hourly Italian Air Force dataset. A method is discussed to obtain daily mean cloud amounts avoiding biases due to missing observations: less than 2 % of the days have no observations, but more than 20 % of them have at least one missing value. Trend analysis is applied to regional Northern and Southern Italy average series. Seasonal and annual trends were estimated by means of least squares linear fitting. Significance was tested using the non parametric Mann-Kendall test. The results show that there is a highly significant negative trend in total cloud amount all over Italy. It is evident in all seasons and is particularly steep in winter where both in Northern and Southern Italy the decrease exceeds 1 okta in 50 years.

In order to obtain information about the copolymerization process of vinyltrimethyl silane with comonomers of different chemical structure, copolymers containing vinyltrimethylsilane and methyl methacrylate at different compositions were synthesized and characterized. Comparison of the reactivity ratios of the resulting copolymers with those containing N-vinyl-2-pyrro-lidone and 2-vinylpyridine previously reported and other related comonomers with different chemical structure allows us to establish some reactivity structure relationship and a generalization for these systems. The monomer reactivity ratios r1 and r2 (MRR) were estimated by using the classical linear fitting procedures and also through a computer program based on a nonlinear minimization algorithm, starting from the r1 and r2 values obtained by the former procedures.

Copolymers containing vinyltrimethoxysilane (VTMOS) and 2-vinylpyridine (2VPy) at different compositions were synthesized and characterized. The monomer reactivity ratios r1 and r2 were estimated by using the classical Fineman-Ross and Kelen Tudos linear fitting procedures. Moreover, these parameters were also estimated using a nonlinear computational fitting known as Reactivity Ratios Error in Variable Method (RREVM). Attempts to obtain the corresponding copolymer with vinyltrimethylsilane (VTMS) were performed but only hompolymerization 2VPy is observed due to the non-reactivity of VTMS under this conditions. The results were analysed in terms of the relative comonomeric structures and compared with similar related systems. The reactivities are interpreted in terms of the resonance and stabilization effects together with the chemical structure.

Measuring dust extinction in high-redshift galaxies is fundamental to estimate the star formation rate density and constrain galaxy evolution models. I measure dust extinction in Lyman break galaxies at z ~ 3 where a broad peak in the star formation rate density is thought to occur. On the basis of image simulations I perform a new method for accurate extraction of colours from images with different point spread functions. Taking advantage of a new colour selection criterion I select a sample of 225 LBGs at redshift ~ 3.2. The UV slope of the sampled galaxies is determined by a linear fit of the observed magnitudes through a proper set of filters coherently with the original definition of the slope β. By performing measurements of β through IZY filters I find −1.79; moreover I find that the β value strongly depends on the set of filters I use for linear fitting. I find a good agreement comparing the three bands fit in our sample with CANDELS GOODS-South data set at the same redshift. UV slope value fits well in the trend for which dust extinction increase at decreasing redshift.

While a large portion of pharmaceutical stability data is known to follow an exponential model decay, linear modeling of this data for expiry estimation is the norm. Expiry predictions based on linear and exponential fits to stability data were made to estimate the bias due to the linear fitting. It was found that within the usual expiry limits on drug potency, the difference between the model fits is relatively trivial. In cases of loss of potency greater than 15%, small assay variability, or great disparity between the length of the study and the time of expiry prediction, however, there is a nontrivial difference in the predictions and the exponential model is preferable.

An electric-field method is developed for measuring the polar anchoring energy of vertically aligned nematic liquid-crystal cells. Both theoretical analyses and confirming experimental results are presented. Vertically aligned liquid-crystal cells with buffed polyimide alignment layers are used to investigate the measurement techniques. Based on the voltage-dependent transmittance of the liquid-crystal cells, a linear fitting can be obtained, leading to a precise determination of the anchoring energy. If some specific liquid-crystal material parameters are known, measuring of the cell capacitance is not necessary.

The capacitance transients caused by hole emissions from Fe-related deep levels were measured in GaAs and GaAs0.77P0.23 at different temperatures. Non-exponential transients were investigated under different conditions and found to relate to the alloy random effect. The transients were decomposed using a Laplace defect spectroscope (LDS). The three well-resolved sharp peaks in the LDS spectra of GaAs0.77P0.23 were assigned to the fine structures of the Fe-related deep levels. The activation energy differences of the fine structures were determined by linear fitting of the slopes of temperature dependences of hole emission rates. The results suggest that the local composition fluctuation in the nearest neighbors of Fe atoms is likely to be responsible for the fine structures.

The binding of 1,25-dihydroxyvitamin D3 [1,25(OH)2D3] to its chick intestinal receptor does not fit well to the linear regression line of Scatchard's model (r = -0.79; dissociation constant, Kd = 0.51 nM). In fact, a concave 'hook' curve describes the data better. By using the Hill analysis the linear fitting was improved (r = 0.99), the Kd was found to be 0.14 nM and the Hill coefficient (nH) 1.42, which indicates a positive cooperativity in the binding of 1,25(OH)2D3 to its receptor. Further we found that Kd and nH are strongly correlated (p less than 0.001). These data suggest the existence of two ligand binding sites located in subunits for the 1,25(OH)2D3 receptor.

To improve the computer determination of thoracic gas volume (TGV), two new approaches were worked out. 1) A new program was designed, which overcomes the difficulties encountered in the time recognition of the panting maneuver and rules out the artifacts. Such a procedure is based on the data analysis in the pressure-volume time derivatives plane. 2) A hyperbolic fitting of the signals recorded during the panting maneuver was introduced. This last procedure, lying on Boyle's law, has proved to be useful in case of large mouth pressure changes. In fact the error induced by the conventional linear fitting may reach 500 ml (9% of the TGV value).

The paper presents a computer-based system for performance and analysis of the single-breath nitrogen washout test (Sb-N2 test). A pneumotachometer and a rapid gas analyser are used for volume flow rate and nitrogen fraction measurements. The data are acquired and analysed by a PDP-11/34 computer. Several sources of measurement errors are considered. An algorithm is proposed to reduce errors in flow measurements due to viscosity variation in respired air. The algorithm for closing volume (CV) detection and calculation of other Sb-N2 parameters is developed from 50 tracings of 18 subjects. The CV is obtained by an iterative linear fitting of the later half of the Sb-N2 curve. Comparisons between computer and hand measurements of three trained readers show good correlations (r = 0.87, 0.93, 0.91). The variability of computer CV measurements was comparable with that of the hand reader with the lowest variance. The coefficient of variation of residual volume and slope of alveolar plateau measurements are apparently reduced. The results demonstrate the adequacy and convenience of using the computer to analyse the Sb-N2 test and indicate that the automation allows for reduction of experimental errors and of test parameter variabilities.

An accurate method for background-correction in two-dimensional data sets, i.e. energy-time or energy-energy (coincidence) matrices, is presented. It is based on linear fitting in the dependent parameter, whence its name LINGAT. Examples show that this method is far superior to the classical peak-minus-background method, albeit more tedious to use. The advantages lie in its ability to separate close-lying peaks in energy and in background. The use of the error spectra in time analyses is discussed.

Upper mantle velocity structure in the Ryukyu and Taiwan-Luzon Island arc regions of the northwest Pacific has been determined to a depth of about 255 km from the analysis of P and S wave travel times data of 106 earthquakes with focal depths varying from 35 to 255 km. Wave velocities were obtained at the depths of foci of earthquakes, in the inclined seismic zones in these regions, by using KAILA's (1969) analytical method. By a linear fitting of velocity variation with depth, the following results were obtained. In the Ryukyu arc region, P velocity increases from 8.01 km/s at 40 km depth to 8.43 km/s at 255 km depth, and S velocity increases from 4.32 km/s at 40 km depth to 4.53 km/s at 255 km depth. In the Taiwan-Luzon region also, P velocity increases from 8.00 km/s at 40 km depth to 8.38 km/s at 240 km depth, and S velocity increases from 4.41 km/s at 40 km depth to 4.50 km/s at 180 km depth. Thus, the P velocity functions in the two regions are quite similar and reveal velocities which are about 5 % higher (on an average) than those in the Shikoku and Kyushu Islands of the southwest Japan region. However, the S velocities in the Taiwan-Luzon region are 2 to 3 % higher than those in the Ryukyu and the southwest Japan regions. There is no evidence for the presence of a significant low velocity Iayer in the inclined seismic zones beneath the Ryukyu and the Taiwan-Luzon arcs.

Extracting parameters iteratively from two component exponential decays requires initial guesses. These are avoided if the treatment is made linear. In practice it is found that the method is badly biased or fails where it is most necessary, i.e., where the decay rates (lifetimes) are close. The origins of the difficulties are detailed and explained with the aid of analyses of simulated decays. Ways of broadening the regions of applicability of the non-iterative method are given.

In this work we studied the nature of the near-neighbour environment in ternary and pseudoternary defect chalcopyrites of the AB 2 X 4 family by using the extended X-ray absorption fine structure (EXAFS) technique. The EXAFS was measured at the K-edge of Zn, Ga and Se elements in ZnGa 2 (S x Se 1-x ) 4 and Ga and Se edges in CdGa 2 (S x Se 1-x ) 4 mixed crystals.NN distance were determined for all the compositions by a linear fitting of differences of phases and by a fitting procedure in k-space. We found bond lenghts nearly constant and close to the respective distances in the end member crystals over all the composition range, whereas the unit cell parameter a(x) changes accordingly to the virtual crystal approximation (Vegard's law).

A phase subdivision of absolute coding grating is proposed to improve the resolution and precision of displacement measurement. The used grating consists of multiple code channel grating of Gray code, and the basic code channel is high frequency Rochi grating. Fourier analysis method is adopted to extract the phase value of grating in decoding, and the wrapped phase distribution of basic code channel is obtained by Fourier transform, filtering, and inverse Fourier transform, then the unwrapped phase distribution could be recovered using the phase order information of Gray code. High resolution of phase subdivision can be achieved via linear fitting of phase distribution. Analysis of the basic principle and the subdivision of the phase to improve the resolution of displacement measurement have also been described in this paper. Experimental results show that the resolution and precision of absolute coding grating is enhanced greatly after phase subdivision and calibration.

Linear least xi/sup 2/-fits will in general give wrong results to the data since the errors are not properly handled. In this note we discuss a solution for this problem. This paper covers briefly the standard X/sup 2/-fitting of trajectory parameters and discusses the case of linear correlations between independent measurements which are all subject to stochastic noise. An analytic solution for unbiased fits including the error analysis is derived. Examples are presented. The mathematical analysis is involved and possibly not of a general interest. The fit methods are available as general software packages on the MCC/SLC-VAX. Similar packages were produced for the HP 28 S pocket calculator for testing purposes. The methods were successfully applied for online monitoring of dispersion functions and transfer-matrix elements. 3 figs.

We report the calculation of boiling points for several alkyl alcohols through the use of improved molecular descriptors based on the optimization of correlation weights of local invariants of graphs. As local invariants we have used the presence of different chemical elements (i.e. C, H, and O) and the existence of different vertex degree values (i.e. 1, 2, 3 and 4). The inherent flexibility of the chosen molecular descriptor seems to be rather suitable to obtain satisfactory enough predictions of the property under study. Comparison with other similar approximation reveals a very good behavior of the present method. The use of higher order polynomials do not seem to be necessary to improve results regarding the simple linear fitting equations. Some possible future extensions are pointed out in order to achieve a more definitive conclusion about this approximation., Facultad de Ciencias Exactas